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Article(id=1235553557596926316, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1235553554455392591, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2021.05.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1594742400000, receivedDateStr=2020-07-15, revisedDate=1599408000000, revisedDateStr=2020-09-07, acceptedDate=null, acceptedDateStr=null, onlineDate=1772508523606, onlineDateStr=2026-03-03, pubDate=1621440000000, pubDateStr=2021-05-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1772508523606, onlineIssueDateStr=2026-03-03, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1772508523606, creator=13701087609, updateTime=1772508523606, updator=13701087609, issue=Issue{id=1235553554455392591, tenantId=1146029695717560320, journalId=1149653034449285133, year='2021', volume='54', issue='5', pageStart='1', pageEnd='108', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1772508522857, creator=13701087609, updateTime=1773989531393, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241765354544890513, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1235553554455392591, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241765354544890514, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1235553554455392591, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=78, endPage=84, ext={EN=ArticleExt(id=1235553559220121972, articleId=1235553557596926316, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Breakdown Voltage and Its Influencing Factors of Thermal-aged Oil-impregnated Insulating Paper Under Pulsating DC Voltage, columnId=1190369198472794288, journalTitle=Insulating Materials, columnName=Insulation Technology, runingTitle=null, highlight=null, articleAbstract=

Firstly, oil-impregnated insulating papers with different ageing states were prepared, and their breakdown voltages under pulsating DC voltage were measured and compared with AC and DC breakdown voltage. The polymerization degree, moisture content, mesopore distribution, and crack characteristics of oil-impregnated insulating papers were measured to explore the possible influencing factors of breakdown voltage under different ageing states. The results show that the AC breakdown voltage is the smallest, and the pulsed DC breakdown voltage (r=1/5) is the largest before failure of oil-impregnated insulating papers. During thermal ageing process, the breakdown voltage fluctuates occasionally or even increases. Compared to AC breakdown voltage, the breakdown voltage under DC and pulsed DC voltages (r=1/5 and 1/3) shows opposite trends with ageing time. The water content and oil absorption capacity of oil-impregnated insulating papers, and the damage to the paper structure are the reasons causing the breakdown voltage to change with ageing time, but the importance of reasons vary with the ageing state.

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本研究首先制备了不同老化状态的油浸绝缘纸，在脉动直流电压下测量其击穿电压，并与交流击穿电压和直流击穿电压进行比较。通过测定油浸绝缘纸的聚合度、水分含量、介孔分布和裂缝特征，探讨不同老化状态下击穿电压的可能影响因素。结果表明：交流击穿电压最小，脉动直流击穿电压（脉动系数r=1/5）在油浸绝缘纸失效之前最大。在热老化过程中，击穿电压偶尔波动甚至升高，在直流电压和脉动直流电压下（r=1/5和1/3）的击穿电压随老化时间的变化趋势与交流击穿电压相反。油浸绝缘纸的含水量、吸油能力、纸结构的损伤都是导致击穿电压随老化时间变化的原因，但各因素影响的重要性随老化状态的不同而不同。

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姚德贵（1971-），男（汉族），安徽芜湖人，高级工程师，博士，主要从事电磁环境监测与评价等方面的研究。

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姚德贵（1971-），男（汉族），安徽芜湖人，高级工程师，博士，主要从事电磁环境监测与评价等方面的研究。

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姚德贵（1971-），男（汉族），安徽芜湖人，高级工程师，博士，主要从事电磁环境监测与评价等方面的研究。

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热老化温度/℃老化时间/天
1202,4,7,10,22,35,60,120,180
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热老化温度及老化时间

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热老化温度/℃老化时间/天
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热老化油浸绝缘纸在脉动直流电压作用下的击穿电压特性及影响因素研究
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姚德贵 1 , 张洋 1 , 王飞鹏 2 , 黄镜亮 2 , 景中炤 3 , 吕中宾 1
绝缘材料 | 绝缘技术 2021,54(5): 78-84
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绝缘材料 | 绝缘技术 2021, 54(5): 78-84
热老化油浸绝缘纸在脉动直流电压作用下的击穿电压特性及影响因素研究
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姚德贵1, 张洋1, 王飞鹏2, 黄镜亮2, 景中炤3, 吕中宾1
作者信息
  • 1国网河南省电力公司电力科学研究院，河南 郑州 450000
  • 2重庆大学 电气工程学院 输配电装备及系统安全与新技术国家重点实验室，重庆 400044
  • 3国网河南省电力公司郑州供电公司，河南 郑州 450000

    • 姚德贵（1971-），男（汉族），安徽芜湖人，高级工程师，博士，主要从事电磁环境监测与评价等方面的研究。

Breakdown Voltage and Its Influencing Factors of Thermal-aged Oil-impregnated Insulating Paper Under Pulsating DC Voltage
Degui YAO1, Yang ZHANG1, Feipeng WANG2, Jingliang HUANG2, Zhongzhao JING3, Zhongbin LÜ1
Affiliations
  • 1Electric Power Research Institute of State Grid Henan Electric Power Company, Zhengzhou 450000, China
  • 2School of Electrical Engineering, State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China
  • 3State Grid Henan Electric Power Company Zhengzhou Power Supply Company, Zhengzhou 450000, China
出版时间: 2021-05-20 doi: 10.16790/j.cnki.1009-9239.im.2021.05.012
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摘要
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本研究首先制备了不同老化状态的油浸绝缘纸，在脉动直流电压下测量其击穿电压，并与交流击穿电压和直流击穿电压进行比较。通过测定油浸绝缘纸的聚合度、水分含量、介孔分布和裂缝特征，探讨不同老化状态下击穿电压的可能影响因素。结果表明：交流击穿电压最小，脉动直流击穿电压（脉动系数r=1/5）在油浸绝缘纸失效之前最大。在热老化过程中，击穿电压偶尔波动甚至升高，在直流电压和脉动直流电压下（r=1/5和1/3）的击穿电压随老化时间的变化趋势与交流击穿电压相反。油浸绝缘纸的含水量、吸油能力、纸结构的损伤都是导致击穿电压随老化时间变化的原因，但各因素影响的重要性随老化状态的不同而不同。

击穿电压  /  脉动直流电压  /  热老化  /  油浸绝缘纸

Firstly, oil-impregnated insulating papers with different ageing states were prepared, and their breakdown voltages under pulsating DC voltage were measured and compared with AC and DC breakdown voltage. The polymerization degree, moisture content, mesopore distribution, and crack characteristics of oil-impregnated insulating papers were measured to explore the possible influencing factors of breakdown voltage under different ageing states. The results show that the AC breakdown voltage is the smallest, and the pulsed DC breakdown voltage (r=1/5) is the largest before failure of oil-impregnated insulating papers. During thermal ageing process, the breakdown voltage fluctuates occasionally or even increases. Compared to AC breakdown voltage, the breakdown voltage under DC and pulsed DC voltages (r=1/5 and 1/3) shows opposite trends with ageing time. The water content and oil absorption capacity of oil-impregnated insulating papers, and the damage to the paper structure are the reasons causing the breakdown voltage to change with ageing time, but the importance of reasons vary with the ageing state.

breakdown voltage  /  pulsating DC voltage  /  thermal ageing  /  oil-impregnated insulating paper
姚德贵, 张洋, 王飞鹏, 黄镜亮, 景中炤, 吕中宾. 热老化油浸绝缘纸在脉动直流电压作用下的击穿电压特性及影响因素研究. 绝缘材料, 2021 , 54 (5) : 78 -84 . DOI: 10.16790/j.cnki.1009-9239.im.2021.05.012
Degui YAO, Yang ZHANG, Feipeng WANG, Jingliang HUANG, Zhongzhao JING, Zhongbin LÜ. Breakdown Voltage and Its Influencing Factors of Thermal-aged Oil-impregnated Insulating Paper Under Pulsating DC Voltage[J]. Insulating Materials, 2021 , 54 (5) : 78 -84 . DOI: 10.16790/j.cnki.1009-9239.im.2021.05.012
正文
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0 引言
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电力变压器对输电网络至关重要[1]。油浸绝缘纸作为电力变压器的绝缘介质，在热、湿、氧、酸的作用下会发生降解[2-3]。在这些老化因素中，热是导致油浸绝缘纸老化的主要因素，会降低其机械强度和电气性能。因此，利用油浸绝缘纸的介电性能和物理化学特性进行状态评估对于变压器的安全运行、计划维护和更换至关重要[4]。击穿电压是油浸绝缘纸的重要性能指标，因此研究热老化油浸绝缘纸的击穿特性有助于了解老化对绝缘性能的影响机理。
随着直流输电系统的快速发展，换流变压器引起了研究者的广泛关注。换流变压器中的阀侧绕组承受复杂波形的电压[5]，阀门侧翼梢的对地绝缘承受脉动直流电压[5-10]。在脉动直流电压下，油浸绝缘纸的击穿特性与交流电压下有许多不同[6]。因此，有必要研究这种电压波形下热老化油浸绝缘纸的击穿电压。
油浸绝缘纸及油纸绝缘在交流电压[11-12]、直流电压[13-14]、冲击电压[12,15-18]和脉动直流电压[6,19-20]作用下的击穿电压均有广泛的研究。LI J等[6]研究了在脉动直流电压（脉动系数r为1和1/3）下油浸绝缘纸的击穿电压，结果表明，在60～110℃内，脉动直流电压下的击穿电压介于交、直流击穿电压之间。CHEN Q G等[20]从理论上计算了油纸绝缘在脉动直流电压作用下的电场强度分布，结果表明，当外加电压中含有少量的交流分量时，击穿电压达到最大值，且该最大值与单独的直流电压作用时无显著差异。上述研究使用的都是未老化的油浸绝缘纸，然而关于热老化油浸绝缘纸交流击穿电压的研究较少[12,21-22]。SUN P T等[12]研究发现热老化油浸绝缘纸的交流击穿电压随热老化时间的延长而增大，击穿电压的增加归因于微球的出现和纤维素纤维的断裂，改善了油浸绝缘纸中的电场分布。LIAO R J等[21]测定了110℃下矿物绝缘油和植物绝缘油热老化油浸绝缘纸板的交流击穿电压，发现击穿电压随热老化时间的增加而波动，与聚合度（DP）无明显相关性。唐超等[22]研究了90、110、130℃下矿物绝缘油和植物绝缘油中热老化油浸绝缘纸的交流击穿电压，发现交流击穿电压与油浸绝缘纸的DP和热老化温度之间没有明显的相关性，在热老化过程中，击穿电压先略有下降，然后上升。然而，在脉动直流电压下热老化油浸绝缘纸的击穿电压是否表现出与交流电压下相同的变化趋势，有待进一步研究。
本研究旨在研究热老化油浸绝缘纸在脉动直流电压下的击穿电压及其可能的影响因素。将绝缘纸置入120℃、130℃矿物油中进行热老化，并测量不同老化状态的油浸绝缘纸在脉动直流下的击穿电压。为了进行比较，在交流和直流电压下进行了相同的实验。用油浸绝缘纸的水分含量、与油浸绝缘纸的介孔和裂缝有关的吸油能力，以及油浸绝缘纸的结构破坏来解释击穿电压随老化时间的变化趋势。
1 实 验
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1.1 加速热老化实验
选择中石油克拉玛依25号环烷基矿物油和泰州鑫源电气设备有限公司生产的绝缘纸为原料，绝缘纸厚度为0.13 mm，直径为80 mm。通过加速热老化实验，获得了不同老化状态下的油浸绝缘纸。为了模拟实际变压器油纸的加工过程，控制实验样品的初始状态，首先在50 Pa、80℃的真空干燥室内分别对绝缘油和绝缘纸进行脱气和脱水处理48 h。然后将绝缘纸在50 Pa、60℃的温度下油浸处理 48 h，之后转移到不锈钢容器中，油与纸的质量比为10∶1。最后将密封的容器放入老化箱中进行老化实验，表1列出了热老化温度及老化时间。加速热老化实验的温度根据以下两个原则确定：①温度不应太低，因为低温导致热老化实验耗费的时间过长，无法实现加速热老化；②温度不应太高，因为高温可能会超过绝缘油的闪点，造成安全隐患。所以最终选择了120℃和130℃作为热老化温度。
在对应的老化时间取样，获得不同老化状态的油浸绝缘纸样品，进行击穿电压、水分含量、聚合度、氮气吸附和解吸实验以及扫描电子显微镜（SEM）测试。通过测定油浸绝缘纸的含水量和DP值，研究其与油浸绝缘纸击穿电压的变化是否有强相关性。根据IEC 60814:1997《绝缘液体 油浸纸及油浸纸板 用卡尔·费塞尔自动电量滴定法测定水分》的要求，用Karl-Fischer库仑滴定仪测量油浸绝缘纸的水分含量，测定时为避免外界环境的影响，到达老化时间后立即打开容器取样。依据IEC 60450:2004《新的和老化的纤维素电气绝缘材料的黏均聚合度的测量》的要求对油浸绝缘纸的DP进行测试。通过气相吸附和解吸实验及SEM测试，研究油浸绝缘纸在热老化过程中的介孔分布、气孔和裂纹。
1.2 击穿电压实验装置
击穿电压实验装置如图1所示，由电源、油罐、电极系统和一些测量仪器组成。电源包括一个函数信号发生器和一个高压功率放大器（Trek 50 kV/12 mA）。函数信号发生器提供所需的电压信号，高压功率放大器将电压升高到所需水平。根据IEC 60243:1998标准设计了一个不对称电极系统来测量油浸绝缘纸的击穿电压，如图2所示。
1.3 击穿电压测试
为减少测量误差，测量10次油浸绝缘纸的室温击穿电压，以平均值作为结果。为了便于描述，将电压的峰值视为油浸绝缘纸发生故障时的击穿电压。在试验过程中，对油浸绝缘纸分别施加不同脉动系数的正脉动直流电压。脉动系数r是交流分量UAC的振幅与直流分量UDC的振幅之比，如式（1）所示。图3为脉动系数为1的脉动直流电压的典型波形。本文选择r为1/5、1/3和1，研究脉动直流电压下油浸绝缘纸的击穿电压。
r=UACUDC
2 结果与分析
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2.1 热老化油浸绝缘纸的击穿电压
不同电压波形下油浸绝缘纸击穿电压随老化时间的变化趋势如图4所示。从图4可以看出，在大多数情况下，交流击穿电压最小，直流击穿电压最大，脉动直流击穿电压（r=1/5和1/3）和直流击穿电压之间没有显著差异。当油浸绝缘纸达到其使用寿命时（本文中取DP=150～200[23-24]），即在120℃下老化180天或130℃下老化90天后，这种趋势变得不明显。3种脉动直流电压波形的击穿电压平均值存在微小差异。
在达到使用寿命之前，脉动直流击穿电压保持在较高水平，在两种热老化温度下，随着老化时间的增加，3种脉动直流击穿电压均表现出一定的波动。但直流击穿电压和脉动直流击穿电压（r=1/5和1/3）随老化时间的变化趋势与交流击穿电压的变化趋势相反。对于处于老化早期或中期的油浸绝缘纸，即在120℃下老化时间小于35天或在130℃下老化时间不超过22天时，这种趋势尤其明显。从图4(b)可以看出，老化时间从4天增加到7天，交流击穿电压有所增加，直流击穿电压和脉动直流击穿电压（r=1/5和1/3）均下降，但与未老化的油浸绝缘纸相比它们都保持在较高水平。两种温度下交流击穿电压的变化趋势与文献[21]中的结果相似。
2.2 可能影响击穿电压随老化时间变化的因素
2.2.1 聚合度
采用一阶动力学模型拟合DP与老化时间的关系，如式（2）所示[25]。
1Pt-1P0=kt
式（2）中：P0和Pt分别是未老化和老化时间为t时绝缘纸的DP；k是一个常数。
图5为油浸绝缘纸的DP随老化时间的变化规律。从图5可以看出，在两个老化温度下，DP均随老化时间的增加急剧下降，在DP接近500时，下降趋势相对缓慢。在120℃下老化180天和在130℃下老化90天的油浸绝缘纸DP均低于250。但DP和击穿电压之间没有明显的相关性。当DP从1 265下降到小于400时，击穿电压也没有明显下降，油浸绝缘纸击穿电压的微小变化不能用DP的降低来解释，这与文献[22]的研究结果一致。但当DP达到非常低的水平时，击穿电压往往很低，在此阶段，油浸绝缘纸的结构损坏以及高水分含量足以导致击穿电压的突然降低。这与文献[12]的研究结果不符，主要是由于水分含量和油浸绝缘纸结构的差异造成的。
2.2.2 水分含量
图6为油浸绝缘纸中水分含量随老化时间的变化规律。
从图6可以看出，在老化过程中水分含量有波动，并在油浸绝缘纸接近使用寿命时急剧增加。水分含量会影响油浸绝缘纸的电气强度[26]，由于一些老化油浸绝缘纸的含水量高于文献[12]中的含水量，导致所得结果与文献[12]结果不完全一致。但这无法解释为什么某些水分含量相对较高的油浸绝缘纸具有相对较高的交流击穿电压，如在120℃下热老化2天和60天以及在130℃下热老化2天、7天和10天的油浸绝缘纸，其击穿电压特别是交流击穿电压与未老化的油浸绝缘纸相比并没有下降太多，甚至高于含水量相对较低的油浸绝缘纸。这意味着水分含量并不是影响热老化油浸绝缘纸交流击穿电压的唯一因素，可能存在其他因素抵消了含水量对热老化油浸绝缘纸交流击穿电压的影响。
2.2.3 吸油能力
绝缘纸由大量的纤维素纤维构成，具有很多的孔，孔的直径从几十纳米到几千纳米不等。采用氮气吸附解吸法测量油浸绝缘纸的介孔分布，并用SEM观察其大孔隙，将吸油率与击穿电压的变化趋势联系起来。为了便于讨论和分析，以130℃下老化的油浸绝缘纸为例。
通过氮气吸附和解吸测量研究油浸绝缘纸的多孔性。依据Barrett-Joyner-Halenda（BJH）方法获得孔径分布和孔体积[27]，并通过Brunauer-Emmett-Teller（BET）方法获得比表面积[28]。
图7为130℃下不同老化时间油浸绝缘纸孔径分布随热老化时间的变化规律。从图7可以看出，油浸绝缘纸的孔径均大于15 nm，不同老化状态下的油浸绝缘纸孔径各不相同。
图8为130℃下不同老化时间油浸绝缘纸的单位孔径下的孔体积（dV/dP）峰值。从图8可以看出，老化时间分别为0、2、22天的油浸绝缘纸，对应的dV/dP峰值大于其他老化时间下油浸绝缘纸的dV/dP峰值，说明其孔径和体积较大，这与图9的结果基本一致。图10为不同老化状态的油浸绝缘纸比表面积。从图10可以看出，在热老化过程中，比表面积变化趋势与孔隙体积变化趋势基本一致。
图11为油浸绝缘纸在130℃下热老化不同时间的SEM图。从图11可以看出，在热老化22天后，油浸绝缘纸开始出现直径为数微米的大孔隙或裂缝。随着热老化时间的延长，孔隙和裂缝的直径呈增大趋势。老化时间为90天时，油浸绝缘纸表面出现较大的贯穿裂缝，说明油浸绝缘纸的结构被破坏。
经过长时间的老化，油浸绝缘纸上有许多充满气体的孔。在脱气和浸渍后，这些孔充满绝缘油。油浸绝缘纸的吸油能力对交流击穿电压和直流击穿电压具有不同的影响。设ε1、γ1和ε2、γ2分别是绝缘油和油浸绝缘纸的等效介电常数及电导率，电场强度E(l)与施加在油浸绝缘纸样品上的电压U0之间的关系可以表示为式（3）[12]。
U0=∫Eldl
式（3）中：l是沿电场方向的距离。为简化分析，假设ε1、γ1、ε2、γ2保持不变。当外加电压为交流电压时，电场强度与油浸绝缘纸和绝缘油的介电常数成反比，两者之间的关系可以写成式（4）[22]。
EoilEpaper=ε1ε2
则可以得到绝缘油中与油浸绝缘纸中的电场如式（5）和式（6）所示[12]。室温下，ε1/ε2约为1/2[29]。
Eoil=U01-ε1ε2l0+ε1ε2l
Epaper=U0ε2ε1-1l0+l
式（5）～（6）中：l0是沿电场方向油的总等效厚度。油浸绝缘纸吸收的油越多，l0越大，绝缘油和油浸绝缘纸中的电场强度越低，改善了油浸绝缘纸中的电场分布，导致击穿电压增加。
当施加直流电压时，电场强度与绝缘油和油浸绝缘纸的电导率成反比，式（4）可以改写为式（7）[6]。
EoilEpaper=γ2γ1
则可以得到绝缘油中与油浸绝缘纸中的电场如式（8）、（9）所示[12]。
Eoil=U01-γ1γ2l0+γ1γ2l
Epaper=U0γ2γ1-1l0+l
不考虑水分等因素的影响时，γ1/γ2约为100[29]。l0增加时，绝缘油和油浸绝缘纸中的电场随之增加，从而导致击穿电压降低。因此随着油浸绝缘纸吸油能力的提升，直流击穿电压和交流击穿电压的变化趋势相反。
对于老化时间小于35天的油浸绝缘纸样品，孔体积和比表面积越大，吸油能力越强，导致交流与直流击穿电压存在差异，尽管一些油浸绝缘纸样品的含水量仍然相对较高（约1.8%），老化2、7、10和22天的油浸绝缘纸交流击穿电压与未老化的油浸绝缘纸相比无明显下降，甚至有所增加。油浸绝缘纸吸油能力对交流击穿电压和直流击穿电压的影响相反，因此直流击穿电压和在小脉动因数（r=1/5和1/3）下的脉动直流击穿电压变化趋势与交流击穿电压不同，对于老化4～7天的油浸绝缘纸样品，交流击穿电压增加，而小脉动因数（r=1/5和1/3）脉动直流击穿电压和直流击穿电压降低。
对于老化35～60天的油浸绝缘纸样品，油浸绝缘纸中的介孔孔径和体积不是影响击穿电压的主要因素，应当考虑纤维素纤维中大孔隙或裂缝的影响。介孔被注入绝缘油，改善了油浸绝缘纸样品在交流电压下的电场分布，油浸绝缘纸结构的损伤可能会降低击穿电压，而电场分布的改善在一定程度上平衡了这一影响，与未老化的油浸绝缘纸相比，交流击穿电压降低并不明显。
对于老化90天的油浸绝缘纸样品，油浸绝缘纸的DP很小（约160），结构严重受损，击穿电压急剧下降，在这种老化状态下，油浸绝缘纸结构的损伤成为影响击穿电压的主要因素。在这种老化状态下，水分含量非常高（约2%），而且也有助于降低击穿电压。
3 结论
收起
（1）在热老化过程中，油浸绝缘纸的脉动直流击穿电压和交流击穿电压均会出现波动，在老化早期和中期，与交流电压相比，脉动因数较小（r=1/5和1/3）的脉动直流电压和直流电压下的击穿电压呈现相反的变化趋势。
（2）对于处于老化早期或中期的油浸绝缘纸，击穿电压随老化时间的变化主要受油浸绝缘纸水分含量、与孔体积有关的吸油能力的影响；对于老化中后期的油浸绝缘纸，油浸绝缘纸纤维素纤维之间的大孔隙或裂缝是引起击穿电压发生变化的主要因素；对于达到使用寿命的油浸绝缘纸，主要的影响因素是油浸绝缘纸结构的损坏和较高的水分含量，这两个因素导致3种电压波形下的击穿电压急剧下降。
基金
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  • 国家电网科技项目(5217021900V)
  • 国家自然科学基金资助项目(51377176)
文献
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2021年第54卷第5期
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doi: 10.16790/j.cnki.1009-9239.im.2021.05.012
  • 接收时间：2020-07-15
  • 首发时间：2026-03-03
  • 出版时间：2021-05-20
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  • 收稿日期：2020-07-15
  • 修回日期：2020-09-07
基金
国家电网科技项目(5217021900V)
国家自然科学基金资助项目(51377176)
作者信息
    1国网河南省电力公司电力科学研究院，河南 郑州 450000
    2重庆大学 电气工程学院 输配电装备及系统安全与新技术国家重点实验室，重庆 400044
    3国网河南省电力公司郑州供电公司，河南 郑州 450000
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